In the context of Large Eddy Simulation (LES) of turbulent flows, there is a current need to compare and evaluate different proposed subfilter-scale models. In order to carefully compare subfilter-scale models and compare LES predictions to Direct Numerical Simulation (DNS) results (the latter would be helpful in the comparison and validation of models), there is a real need for a "grid-independent" LES capability and explicit filtering methods offer one means by which this may be achieved. Advantages of explicit filtering are that it provides a means for eliminating aliasing errors, allows for the direct control of commutation errors, and most importantly allows a decoupling between the mesh spacing and the filter width which is the primary reason why there are difficulties in comparing LES solutions obtained on different grids. This thesis considers the design and assessment of discrete explicit filters and their application to isotropic turbulence prediction.

In the context of Large Eddy Simulation (LES) of turbulent flows, there is a current need to compare and evaluate different proposed subfilter-scale models. In order to carefully compare subfilter-scale models and compare LES predictions to Direct Numerical Simulation (DNS) results (the latter would be helpful in the comparison and validation of models), there is a real need for a "grid-independent" LES capability and explicit filtering methods offer one means by which this may be achieved. Advantages of explicit filtering are that it provides a means for eliminating aliasing errors, allows for the direct control of commutation errors, and most importantly allows a decoupling between the mesh spacing and the filter width which is the primary reason why there are difficulties in comparing LES solutions obtained on different grids. This thesis considers the design and assessment of discrete explicit filters and their application to isotropic turbulence prediction.

This thesis focuses on the phenomenon of aliasing and its mitigation with two explicit filters, i.e., Shuman and Padé filters. The Shuman filter is applied to velocity components of the Navier--Stokes equations. A derivation of this filter is presented as an approximation of a 1-D “pure math” mollifier and extend this to 2D and 3D. Analysis of the truncation error and wavenumber response is conducted with a range of grid spacings, Reynolds numbers and the filter parameter, β. Plots of the relationship between optimal filter parameter β and grid spacing, L2-norm error and Reynolds number to suggest ways to predict β are also presented. In order to guarantee that the optimal β is obtained under various stationary flow conditions, the power spectral density analysis of velocity components to unequivocally identify steady, periodic and quasi-periodic behaviours in a range of Reynolds numbers between 100 and 2000 are constructed. Parameters in Pade filters need not be changed. The two filters are applied to velocities in this paper on perturbed sine waves and a lid-driven cavity. Comparison is based on execution time, error and experimental results.